Asymptotically Locally Euclidean metrics with holonomy SU(m)

Journal article

Let G be a nontrivial finite subgroup of U(m) acting freely on C^m - 0. Then C^m/G has an isolated quotient singularity at 0. Let X be a resolution of C^m/G, and g a Kahler metric on X. We say that g is Asymptotically Locally Euclidean (ALE) if it is asymptotic in a certain way to the Euclidean metric on C^m/G. In this paper we study Ricci-flat ALE Kahler metrics on X. We show that if G is a subgroup of SU(m) acting freely on C^m - 0, and X is a crepant resolution of C^m/G, then there is a ...

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Authors: Joyce, D

• Journal: Annals of Global Analysis and Geometry 19 (2001), 55-73.
• Publication date: 1999-05-07
• Keywords: math.AG; math.DG